Official Guide Explanation:
Data Sufficiency #114




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Solution and Metadata

Question: 114
Page: 161
Difficulty: 6 (Moderately Difficult)
Category 1: Geometry > Quadrilaterals >
Category 2: Geometry > Triangles > Multiple figures

Explanation: To find the area, you need the length and the width. Statement (1) is insufficient: you'd need another equation with l and w to solve for the value of each. Statement (2) is also insufficient. Since d is the hypotenuse of a right triangle with sides l and w, you can create this equation:

l2 + w2 = d2

l2 + w2 = 20

Taken together, the statements are sufficient. Given two equations and two variables, even with the squares making the equations non - linear, it's likely you can solve for the area. However, it's worth making sure:

l + w = 6

(l + w)2 = 36

l2 + 2lw + w2 = 36

Now, compare that to the equation from (2):

l2 + w2 = 20

Subtract that equation from the one that preceded it, resulting in:

2lw = 16

lw = 8

That's the area of the rectangle, so the correct choice is (C).

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